Robotics: Getting robots to walk gracefully on two legs is hard. But a new approach could make robots more elegant and versatile

IN RECENT years robots have gone through a rapid evolution: like their human creators, they have gone from crawling on the ground to walking upright on two legs. Indeed, the latest humanoid robots, such as Honda's Asimo and Sony's QRIO, can climb stairs, dance, run and jump. Even the most advanced robots, however, still cannot move with the grace, agility and flexibility of a human.

The problem with current robots is the “zero-moment point” (ZMP) algorithm that controls them, says Jessy Grizzle of the University of Michigan in Ann Arbor. Although ZMP can produce some impressive results, its design requires a low centre of gravity and flat feet, making it unable to emulate the speed and agility of a human gait or to cope with uneven surfaces. Both QRIO and Asimo walk in a crouched position, with their knees permanently bent in an awkward, constipated-looking manner. Their ability to climb stairs is the result of careful choreography and laborious mapping of the environment, says Dr Grizzle.

The ZMP algorithm results in motion that looks unnatural, says Dr Grizzle, because it has no bearing upon how humans actually walk. While taking a step, it requires that the supporting foot is flat on the ground so that balance can be achieved by exerting forces through the ankle joint. Keeping one foot flat in this way makes control of the robot relatively easy, at least in theory. A balance-of-forces calculation at the ankle joint determines the position of the shin, and the process is repeated at the knee to determine the position of the thigh, and so on.

The problem is that the complexity of the calculation grows, roughly speaking, in proportion with the cube of the number of joints in the robot, which quickly becomes computationally unwieldy. This will make life increasingly difficult for the engineers in future as they attempt to add more complex behaviours to their robots' repertoires, says Russ Tedrake, an expert in bipedal locomotion at the Massachusetts Institute of Technology. Which is why a new algorithm devised by Dr Grizzle, called “hybrid zero dynamics” (HZD), is so clever. It simplifies the problem, producing reliable predictions for walking motions which can be applied across a range of robot designs.

Walking humans roll their weight forward from the heel to the ball of the supporting foot, says Dr Grizzle. But while pivoting on this supporting foot, they have no direct way to regulate the rate at which their bodies fall forward. The rate of fall can be regulated only indirectly, by artful positioning of torso and limbs, a skill exemplified by some humans' ability to walk on stilts. So Dr Grizzle designed his algorithm to work with robots that do not have feet or ankles, but simply have two rigid legs, like stilts. Together with Eric Westervelt, a doctoral student, he devised two simple equations. One describes the motion of any complex walking system as a form of inverted pendulum; the other describes how this inverted pendulum will move. The simplicity of these equations, and their ability to make very accurate predictions, ensure that the robot stays balanced.

Remarkably, Dr Grizzle does not have a robot of his own on which to test his algorithm. Instead, it was tested on a two-legged robot called Rabbit at the Laboratoire Automatique de Grenoble in France. Rabbit, it turns out, can walk and run, despite not having any feet. It can recover from being shoved, and can even carry a load equivalent to 30% of its own weight without much reprogramming.

To be fair, Honda's Asimo does not always require its feet to be flat, as the company points out. When Asimo is in its running mode, both its feet lift off the ground between strides. Dr Grizzle responds that it all depends on what you count as “running”. Asimo's steps are less than half the length of its feet, and both feet are off the ground for a mere five milliseconds, he notes. His algorithm produces motion that is far more faithful to the way humans run, with both feet off the ground for 100 milliseconds and a step length of over 60 centimetres. The result, in short, is robotic movements that are much less, well, robotic.